Somewhere in my graduate education I came across the following observation: the role of a selection process isn’t to find the right choice, but to certify one choice over others as the right one. A boxing match that goes the distance and is decided by the judges will produce a winner, but that winner might not have actually been the best fighter that night. As far as the institutional interests are concerned, though, that doesn’t matter: boxing needs a champion more than it needs the right champion.
Keep that in mind as we think about our voting system. Few ideas are as engrained in democratic societies as the notion that elections should decide public debates. The purpose of elections, after all, is to determine which candidate has the proper mandate to govern.
There turn out to be a number of fascinating problems with that. To illustrate, I’m going to have to talk about a few simple concepts that sometimes go by complicated names.
The first is the idea of a Condorcet winner. In an election, the Condorcet winner is the candidate who would win a one-on-one contest against every other candidate in the race. By definition, the winner of a two-person race is always a Condorcet winner; however, in a three-person race this can change radically. If one candidate receives a plurality of votes and her opponents split the opposition, then that candidate might win an election against two candidates, when – in a head-to-head contest – she would have lost that election against either. In such a case, that candidate would not be a Condorcet winner.
This is what has been happening with Donald Trump in a number of Republican primaries, especially early on when the field was so dramatically divided. Failing to select the Condorcet winner is a particular weakness of our winner-take-all electoral system. It is commonly argued that George W. Bush won the White House in 2000 without being a Condorcet winner; the same could be said for Bill Clinton’s 1992 victory and Woodrow Wilson’s win over Teddy Roosevelt in 1912.
One proposed solution to this problem is the alternative vote (also known as instant runoff voting). Under the alternative vote, people rank candidates rather than only voting for one person. The candidates are then ranked in accordance with the number of first-place selections they received. The lowest-performing candidate is eliminated and his votes redistributed to whoever electors picked as their second choice. The process continues until a majority winner emerges.
At first blush, the alternative vote seems to resolve the Condorcet paradox because it helps deal with the problem of spoilers, or candidates whose voters inadvertently help elect their least-preferred candidate. In truth, the math is more complicated than that – especially if there are more than three candidates. Under the alternative vote, it is less likely that a Condorcet winner would lose an election, but it is still possible. And because the math is more complicated, it is harder for voters to understand the risks of failing to vote strategically.
The alternative vote is popular with detractors of our current voting system, helped in part by a popular YouTube video by CGP Grey. Even if it fails to select the Condorcet winner on occasion, the alternative vote does so more often than the winner-take-all system. But the alternative vote also has a second problem that winner-take-all doesn’t: it doesn’t exhibit monotonicity. Briefly, this means that under the alternative vote it is possible to sometimes hurt a candidate by ranking him higher or help a candidate by ranking him lower. Other outcomes seem even more perverse: under some circumstances, for example, the best way to help your preferred candidate under the alternative vote would be to not vote at all.
All of this highlights that what seems like a straightforward task – designing a fair electoral system – is actually fiendishly complicated. Much of the problem comes from the fact that it isn’t entirely clear what we mean by ‘fair’ in the first place. Colloquially, we mean that the most popular candidate should win; in actuality, there isn’t always such a candidate. One interesting wrinkle to the idea of the Condorcet winner is the Condorcet Paradox, which demonstrates that in some races with more than two candidates, a Condorcet winner doesn’t exist at all. In a three-way race where no candidate is preferred to each of the other two, what do we want from our electoral system?
If you believe, as most people seem to, that the role of elections is to give the public the opportunity to voice its will, then the Condorcet Paradox is a real challenge. This is the kind of challenge that ultimately has to be faced by proponents of ‘direct democracy’ and similar schemes: holding a vote isn’t a neutral activity; how you arrange the mechanics of the vote will have a profound impact on the outcome.
In physics, the Heisenberg Uncertainty Principle holds that a system can exist in a multiplicity of mutually incompatible states at the same time, and that only at the moment of observation does it collapse into one of those states. The act of measuring the system forces it into one configuration and not another. That is an uncomfortably apt metaphor for elections. When politicians say that the people have spoken, you might want to ask: sure, but what were they asked?
The next installment in this series will look at the Electoral College and the two-party system. Stay tuned.
Follow Pedro on Twitter @IamPedroA.
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